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Discrete Lotka-Volterra equation over $p$-adic space was constructed since$p$-adic space is a prototype of spaces with the non-Archimedean valuations andthe space given by taking ultra-discrete limit studied in soliton theory shouldbe regarded as a space with the non-Archimedean valuations in the previousreport (solv-int/9906011). In this article, using the natural projection from$p$-adic integer to a ring $Z/p^n Z$, a soliton equation is defined over thering. Numerical computations shows that it behaves regularly.Comment: LaTex, 10 page

The Lotka-Volterra equation over a finite ring ℤ/pNℤ

The Lotka-Volterra equation over a finite ring ℤ/p^Nℤ